Find the solutions of the systemy=x^2+3x-4y=2x+2a. (-3,6) and (2,-4)b. (-3,-4) and (2,6)c. (-3,-4) and (-2,-2)d. no solution

b. (-3, -4) and (2, 6)

Step-by-step explanation:

By the transitive property of equality, if y equals thing 1 and y also equals thing 2, then thing1 and thing 2 are also equal.  So we will set them equal to each other and factor to solve for the 2 values of x:

Get everything on one side of the equals sign, set the whole mess equal to 0, and combine like terms to get:

Because this is a second degree polynomial, a quadratic to be precise, it has 2 solutions.  We need to find those 2 values of x and then use them in either one of the original equations to solve for the y values that go with each x.  

Factoring that polynomial above gives you the x values of x = -3 and 2.  Sub in -3 first:

y = 2(-3) + 2 and

y = -6 + 2 so

y = -4

Therefore, the coordinate is (-3, -4).

Onto the next x value of 2:

y = 2(2) + 2 and

y = 4 + 2 so

y = 6

Therefore, the coordinate is (2, 6)

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: